Answer:
b) There is translation 3 units to the right and 1 unit up
c) The domain is {x I x > 3}
The equation of the asymptote is x = 3
Step-by-step explanation:
* Lets revise the rule of the translation
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Now lets solve the problem
b) ∵ f(x) = [tex]log_{2} (x-3)+1[/tex]
∵ The parent function is [tex]log_{2} x[/tex]
∴ x is changed to (x - 3), that means there is a translation 3 units
to the right
∵ We add the parent function by 1, that means there is a translation
1 unit up
* There is translation 3 units to the right and 1 unit up
c) To find the domain of the function, find the values of x which
make the function undefined
∵ [tex]log_{2}(0)[/tex] is undefined
∴ x - 3 can not be 0
∵ x - 3 = 0 ⇒ add 3 to both sides
∴ x = 3
∴ The domain of the function is all real number greater than 3
* The domain is {x I x > 3}
∵ x can not be 3
∴ There is a vertical asymptote, its equation is x = 3
* The equation of the asymptote is x = 3
# Look to the attached graph for more understand for the domain
and the equation of the asymptote
